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The mathematical problem of minimizing gross solids entrainment in an n-stage evaporator is formulated and solved using the method of Lagrange multipliers. The solution procedure enables direct comparison of the decontamination efficiencies of multistage evaporators as the number of stages (n) is varied. A numerical example is utilized to illustrate the method of solution. Equivalent expressions for batch distillation are also derived.

An analytical method is herein developed to evaluate the stress field in the critical regions of a U-tube subject to differential thermal expansion. The solution is intended to be used as a design tool to conveniently study the variation of geometric parameters on the U-tube stress distribution. Those design variables which have significant effects on the structural characteristics of the U-tube are identified by an in-depth study of a typical example problem. Some effective design remedies are also discussed.